Question

If you dilate triangle XYZ to form X'Y'Z' using a magnitude (scale factor) of 2 and a center dilation at the origin, what are the coordinates of the dilated triangle?
Triangle XYZ points:
Point X: (2, 4)
Point Z: (7, 2)
Point Y: (6, 0)

Answer 1

To dilate triangle XYZ to form triangle X'Y'Z' with a scale factor of 2 and a center of dilation at the origin (0, 0), we multiply the coordinates of each vertex by the scale factor.

Here are the calculations for each point:

1. **Point X (2, 4)**:
\[
X' = (2 \times 2, 4 \times 2) = (4, 8)
\]

2. **Point Y (6, 0)**:
\[
Y' = (6 \times 2, 0 \times 2) = (12, 0)
\]

3. **Point Z (7, 2)**:
\[
Z' = (7 \times 2, 2 \times 2) = (14, 4)
\]

Now, we can summarize the coordinates of the dilated triangle X'Y'Z':

- Point X': (4, 8)
- Point Y': (12, 0)
- Point Z': (14, 4)

Thus, the coordinates of the dilated triangle X'Y'Z' are:
- X' = (4, 8)
- Y' = (12, 0)
- Z' = (14, 4)